brainpopfandomcom-20200223-history
Distance, Rate, and Time/Transcript
Transcript Title text reads: The Mysteries of Life with Tim and Moby Tim and Moby are standing on an empty train platform. There’s no sign of a train for miles. Moby looks at his wrist watch and beeps. TIM: Yup. I guess our train's late. A letter appears. Text reads as Tim narrates: Dear Tim and Moby, Can you help me with distance, rate, and time problems? From, Jack TIM: I have trouble with those too, but they’re not so bad once you take them apart. The first thing to know is the formula, distance equals rate times time. A formula appears, reading, d, equals r, times t. TIM: We can also say that rate equals distance divided by time, and time equals distance divided by rate. On-screen, two more formulas appear, reading, r, equals d, over t, and t, equals d, over r. Moby beeps. TIM: This formula can help you solve all sorts of problems. Moby beeps. TIM: Well, like problems involving distance, rate, and time. Listen: Two trains are traveling in between Detroit, Michigan, and Los Angeles, California, on the same track. On-screen, two trains speed toward each other from opposite directions. TIM: Their trips start at the same time. On-screen, digital clocks appear below each train. Both read, 10:45. TIM: The track is 3,600 kilometers long. On-screen, a map of the U S, appears. A dotted line connects Detroit and Los Angeles. TIM: Train A, is traveling from L A, to Detroit at a rate of 80 kilometers per hour. On-screen, a speedometer appears beneath the eastbound train, showing a speed of 80 kilometers per hour. TIM: Train B, is flying along from Detroit to L A, and at 100 kilometers per hour. On-screen, a speedometer appears beneath the westbound train, showing a speed of 100 kilometers per hour. TIM: How long will it take for the two trains to meet? It’s a good idea to read the problem a few times before you do anything. On-screen, a scrap of paper with the written problem appears. TIM: Okay. We need to draw a diagram. We know that the length of track from L A, to Detroit is 3,600 kilometers, so let’s put that in. On-screen, a line is drawn on a piece of paper. One endpoint is marked, L A, and the other is marked, Detroit. Text beneath the line reads, 3,600 kilometers. TIM: And we know that Train A, is starting in L A, and Train B, is starting in Detroit. On-screen, a train marked, A, is drawn above the endpoint marked, L A. A train marked, B, is drawn above the endpoint marked, Detroit. TIM: We know that, A, is traveling at a rate of 80 kilometers per hour and B, is traveling at a rate of 100 kilometers per hour. On-screen, an arrow marked, 80 k p h, is drawn above train A, pointing east. An arrow marked, 100 k p h, is drawn above train B, pointing west. Moby beeps. TIM: Right, now we build an equation. On-screen, a table with 2 rows and 3 columns appears. The rows are marked, L A, to Detroit, and Detroit to L A. The columns are marked, rate, time, and distance. TIM: We know the rates. On-screen, the table's rate column is filled with the values, 80 k p h, and 100 k p h. TIM: And we don’t know the times yet, but we do know that each train will travel for the same amount of time. Moby beeps. TIM: Well, they both left at the same moment, so when they meet, they'll have been traveling for the same amount of time. The unknown travel time of each train can be expressed by the variable, t. On-screen, the table's time column is filled with the values, t, and t. TIM: If rate times time equals distance, then the distance train A, travels is 80 t, and the distance train B travels is 100 t. On-screen, the table's distance column is filled with the values, 80 t, and 100 t. TIM: We know one other thing: the distance between Detroit and L A, is 3,600 kilometers. So the distance each train travels before they meet up with each other has to equal 3,600 kilometers. And there is our equation, 80 t, plus 100 t, equals 3,600. An equation appears, reading, 80 t, plus 100 t, equals 3,600. TIM: We just have to solve for t. On-screen, the equation becomes, 180 t, equals 3,600. Both sides of the equation are divided by 180, leaving, t equals 20. Moby beeps. TIM: Let’s go back to our table and plug in our t value. On-screen, the values in the table's time column are replaced with, 20 hours. TIM: So in 20 hours from the time they left, train A, will have traveled 1,600 kilometers, and train B, will have traveled 2,000 kilometers. On-screen, the values in the table's distance column are replaced with, 1,600 kilometers, and 2,000 kilometers. TIM: They will meet at the point on that track that is 1,600 kilometers from L A, and 2,000 kilometers from Detroit. So, our answer is: The trains will meet 20 hours after they left. There! Just remember that distance equals rate times time, and you'll do okay. Hey, what time is our train supposed to be here? Moby beeps. He pulls out a pencil and notepad and begins to scribble. TIM: Why don't we just look at the schedule? On-screen, Tim looks up at the departure board. Moby puts the pencil and notepad away. A train whistle sounds in the distance. Category:BrainPOP Transcripts